Microwave sensor using autler-townes splitting

ABSTRACT

A microwave sensor determines an electric-field strength of a microwave field populated by quantum particles in an ultra-high vacuum (UHV) cell. A probe laser beam and a coupling laser beam are directed into the UHV cell so that they are generally orthogonal to each other and intersect to define a “Rydberg” intersection, so-called as the quantum particles within the Rydberg intersection transition to a pair of Rydberg states. The frequency of the probe laser beam is swept so that a frequency spectrum of the probe laser beam can be captured. The frequency spectrum is analyzed to determine a frequency difference between Autler-Townes peaks. The electric-field strength of the microwave field within the Rydberg intersection is then determined based on this frequency difference.

This invention was made with government support under grant numberFA8650-19-C-1736 awarded by the U.S. Air Force. The government hascertain rights in the invention.

BACKGROUND

Microwaves have many applications including those in point-to-pointcommunication links, satellite and spacecraft communication, remotesensing, radio astronomy, radar, and medical imaging. “Microwave”, asbroadly defined herein, encompasses electromagnetic radiation ofwavelengths of one meter (corresponding to a frequency of 300 megahertz(MHz)) down to 100 micrometers (corresponding to a frequency of threeterahertz (THz)); in other words, “microwave”, as defined herein,encompasses ultra-high frequency (UHF), super high frequency (SHF),extremely high frequency (EHF), also known as “millimeter wave”, andtremendously high frequency (THF) frequency ranges defined by theInternational Telecommunications Union (ITU).

In many microwave applications, it can be important to determine thepropagation direction and electric-field strength of a receivedmicrowave vector. Herein, “microwave vector” refers to a propagatingmicrowave field or field component that can be characterized by acombination of 1) a propagation direction that corresponds to theorientation of the vector; and 2) an electric-field strength thatcorresponds to the magnitude of the vector. If the vector isinformation-bearing, then it qualifies as a microwave “signal”. Forexample, characterizing the direction and strength of aninformation-bearing microwave signal can be used to locate itstransmitter, e.g., to orient a receiver's antenna or for geolocationpurposes.

While microwave sensors have been realized using a variety oftechnologies, performance has been limited by a lack of sensitivity.What is needed is an approach to microwave sensing that provides forgreater sensitivity in direction and intensity measurements.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of a microwave sensor using Rydbergparticles to achieve high sensitivity characterization of microwavevectors.

FIG. 2 is a perspective view of a particle handler of the sensor of FIG.1 .

FIG. 3 is a schematic diagram showing how the sensor of FIG. 1characterizes microwave vectors.

FIG. 4A is a top schematic plan view of a front-side lenslet array of adiscrete lenslet array (DLA) that serves as a microwave lens in thesensor of FIG. 1 .

FIG. 4B is a bottom schematic plan view of a back-side lenslet array ofthe DLA.

FIG. 4C is a schematic elevational view of the DLA showing delayelements that couple lenslets of the front-side array with respectivelenslets of the back-side array.

FIG. 5 is an energy diagram showing different states of a particle, inthis case, a rubidium 87 atom, used by the sensor of FIG. 1 to evaluatethe intensity of microwave vectors.

FIG. 6 is a graph comparing spectra of a probe laser beams showinglaser-beam intensity as a function of frequency detuning both in theabsence of a microwave field and in the presence of a microwave field.

FIG. 7A is a graph comparing three transmission spectra for differentmicrowave vector intensities, illustrating how microwave intensity canbe determined from a frequency spectrum.

FIG. 7B is a graph showing, for four different frequencies, linearrelations between microwave field strength and Autler-Townes frequencydifferences.

FIG. 8 is a graph showing that, for most microwave frequencies, there isa corresponding pair of Rydberg states of Cesium 133 atoms that can beused for determining microwave field strength.

FIG. 9 is a flow chart of a process for determining vector direction andintensity using the sensor of FIG. 1 and other systems.

FIG. 10A is a schematic perspective view of a 3D microwave sensor systemfor obtaining a three-dimensional intensity profile of a microwavefield.

FIG. 10B is a schematic illustration of the 3D sensor system of FIG. 10Ashowing a dichroic mirror used to align a probe laser beam and acoupling laser beam so that they counter-propagate.

FIG. 10C is a flow chart of a 3D microwave sensor process implementableusing the 3D microwave sensor system of FIG. 10A.

FIG. 11A is a schematic illustration of a sensor using thermal particles(as opposed to cold particles).

FIG. 11B is a schematic illustration of the sensor of FIG. 11A showinghow the frequency spectra resulting from on-axis and off-axis incidentmicrowave vectors differ.

DETAILED DESCRIPTION

In accordance with the present invention, a microwave sensor measuresthe electric-field strength of a microwave field based on a frequencydifferential between Autler-Townes peaks, that, is transmission peaksresulting from Autler-Townes splitting. A probe laser beam and acoupling laser beam intersect with a microwave field populated byquantum particles, e.g., alkali atoms. The frequency of the probe laserbeam is swept and captured to provide a probe laser beam frequencyspectrum from which the frequency differential can be determined. Theelectric-field strength of the microwave field at the Rydbergintersection can then be determined from the frequency differential.

The probe laser beam and the coupling laser beam intersect within aparticle cloud excite quantum particles (i.e., neutral or charged atomsor molecules) into a superposition of a ground state and a Rydbergstate. Herein, the volume within which the laser beams intersect isreferred to as a “Rydberg intersection” to emphasize its characteristiccontents. Effectively, the Rydberg intersection defines the location ofa microwave detector having high sensitivity and low noise. The probeand coupling beams can be steered so as to move the Rydberg intersectionwithin the particle cloud to obtain an electric-field strengthdistribution for the microwave field.

As shown in FIG. 1 , a microwave sensor 100 includes a particle handler102, a laser system 104, a magnetic-field generator 106, a microwavelens 108, a camera 110, and an image analyzer 112. Camera 110 and imageanalyzer 112 function together as a spectrum analyzer.

Particle handler 102 includes a particle dispenser 114 in a sourcechamber 116, a manifold including an ion pump 118 and a particle cloudchamber 120. Particle cloud chamber 120 is an ultra-high vacuum (UHV)cell serving to isolate a particle cloud from the environment. Microwavelens 108 is located at the top or front end of particle handler 102 andadjacent to particle-cloud chamber 120. Laser system 104 includes aprobe laser 130, one or more coupling lasers 132, a frequency scanner134, a laser steering module 136, and a magneto-optical trap (MOT) laser138. Particle handler 102, shown in perspective in FIG. 2 , can be basedon a RuBECi® system available from ColdQuanta Inc.

Particles are released from particle dispenser 114, expanding intosource chamber 116. In the illustrated embodiment, the particles arerubidium 87 atoms (⁸⁷Rb). Alternatively, the particles can be cesium 133(¹³³Cs) atoms, other isotopes of rubidium or cesium, other alkali atoms,non-alkali atoms, ions, or neutral or charged molecules. Particles exitsource chamber 116 through a pinhole 122 into the manifold including ionpump 118. Ion pump 118 helps maintain an ultra-high vacuum (UHV) inparticle cloud chamber 120, while pinhole 122 supports a pressuredifferential relative to a weaker vacuum for source chamber 116.Magnetic-field generator 106 and MOT laser 138 establish amagneto-optical trap 140 that confines particles in chamber 120 so thatthey form a cloud 142. MOT 140 can be a two-dimensional (2D) MOT, asix-beam 2D MOT, a three-dimensional MOT (3D MOT), or any one of avariety of suitable MOTs or optical traps. A MOT can trap cold particlesto achieve a dense population so that high spatial resolution can beattained.

Microwave lens 108 is designed to focus incoming microwave vectors (withplanar wavefronts) onto a focal surface 150 within particle-cloudchamber 120. As shown in FIG. 1 , focal surface 150 extends throughparticle cloud 142. For example, a “received” far-field microwave vector152 can arrive at microwave lens 108. Microwave lens 108 can retransmitthe received microwave vector 152 to yield retransmitted microwavevector 154 in cloud chamber 120 that is focused on a spot 156 on focalsurface 150. An electric-field strength of the incoming microwave vectorcan be determined from the intensity of the focused “image” of thatvector at focal surface 150. In alternative embodiments, the microwavelens manipulates the incident radiation in other ways.

The coupling of the atom-lens system allows for information contained inthe microwave vector to be converted to a measurable signal on theatoms; for example, the lens can be used to convert phase informationfrom the vector into spatial information in the cloud, etc.). In thecase of the illustrated simple lens, the location of spot 156 isdetermined by the angle of incidence of the received microwave vector152. Accordingly, the direction of the received microwave vector can bedetermined as a function of the location of the focal spot 156 on focalsurface 150. As shown in FIG. 3 , second microwave vector 352 having adifferent direction than microwave vector 152 results in a transmittedmicrowave vector 354 with a focal spot 356 at a different location offocal surface 150. In effect, microwave lens 108 applies a Fouriertransform to incoming far-field microwave vectors; reversing the Fouriertransform allows the direction of the received microwave vectors to becharacterized from the locations of the respective focal spots on focalsurface 150.

In the illustrated embodiment, microwave lens 108 is designed for amicrowave or, more specifically, a millimeter-wave, frequency of 104.7gigahertz (GHz). Microwave lens 108 is implemented as a discrete lensletarray (DLA) including a front-side (receiving) antenna array 360 and abackside (transmitting) antenna array 362. Front-side antenna array 360samples the incident W-band field at a Nyquist spatial frequency (λ/2,where λ is the free-space wavelength). As shown in FIG. 4A, front-sidearray 360 is an 18 mm 8×8 square array of 64 antenna elements 460. Asshown in FIG. 4B, back-side array 362 is a matching 18 mm square 8×8array of 64 antenna elements 462. In alternative embodiments, differentarray dimensions are used, e.g., 10×10. Also, some alternativeembodiments use physical optics instead of or in addition to DLAs.

As indicated in FIG. 4C, each antenna element 460 of front-side array360 is coupled to a respective antenna element 462 of back-side array362 via a respective delay circuit 464 of an array of delay circuits466. The amount of delay imposed by delay circuits 464 varies spatiallyin that relatively central delay circuits impose a greater delay thanrelatively peripheral delay circuits.

In other embodiments, the antenna elements of the two arrays aredistributed irregularly within their respective array to minimize imageartifacts. Furthermore, the antenna elements of one array are notaligned with those of the other array. The number of antenna elementsfor one array can equal the number of the other array, respective pairsof antenna elements can be coupled respectively through a like number ofdelay elements.

The focal length for microwave lens 108 is 15 mm, with an acceptablevariance of ±3 mm. This focal length is suited for a frequency range of90 GHz to 110 GHz, which includes the target frequency of 104.7 GHz. DLA108 creates a flat focusing surface, which allows for a simpler imagingsystem (i.e. using one CCD camera versus using two CCD cameras) toextract the complete vector information of the incoming microwave field.In alternative embodiments, other focal lengths are used, e.g., tocorrespond to different frequencies, working distances, and apertures.

Microwave lens 108 implements a discrete Fourier transform (DFT) so asto focus planar wavefronts to respective spots in the focal curve; thisis useful for far-field applications such as radar and communications.For near-field applications such as brain imaging and biologicalsensing, the microwave lens focuses diverging wavefronts to respectivespots on the focal surface; for these near-field applications, transferfunctions other than Fourier transforms can be used. Typically, multiplesimultaneous incident waves form a non-uniform power densitydistribution on the focal surface.

Backside antenna array 362 (FIG. 4B) is formed on a substrate 470 ofhigh-resistivity silicon so as to leave a 2.0 mm border 472, which is tobe anodically bonded to cloud particle cell 122. Cell 122 has outerdimensions of 23 mm×23 mm×61 mm, and an internal cross section of 20mm×20 mm. In other embodiments, different specifications apply.

The design parameters of the DLA (focal length and shape of the focusingsurface) are selected to match the position of the focal spot with thesize and the position of the cloud of Rydberg atoms inside the vacuumcell. The design is diffraction limited to operate the DLA at a targetfrequency of 104.7 GHz, which corresponds to the transition betweenRydberg states 28D_(5/2) and 29P_(3/2) in rubidium. So as to matchback-side antenna array 362, front-side antenna array 360 (FIG. 4A) isformed on a substrate 474 so as to leave a 2.0 mm border 476.

The field strength of microwave vector 154 (FIG. 1 ) can be determinedfrom its impact on the transmission spectrum of a probe laser beam 160from probe laser 122. With reference to the energy-level diagram of FIG.5 , in the absence of a coupling beam and a microwave signal, a 780nanometer (nm) probe beam is absorbed by ⁸⁷Rb atoms at the targetmicrowave frequency of Ω_(RF)=104.7 GHz. Electrons in a ground state5S_(1/2) transition to a 5P_(3/2) (non-Rydberg) excited state.

A coupling laser beam 162 (FIG. 1 ) from coupling laser 124 can bedirected to intersect probe laser beam 160 so that Rydberg atoms aregenerated in Rydberg intersection 164, which includes the focal spot ofthe retransmitted microwave vector. Rydberg intersection 164 can have acompact shape: 1) large enough so that a strong spectral signal can beobtained; and 2) small enough to resolve the microwave vector ofinterest from microwave vectors coming from slightly differentdirections. To achieve a compact intersection shape, the probe andcoupling beams can be orthogonal or nearly (e.g., ±10°) orthogonal. Inalternative embodiments, plural coupling beams are used; also, in someembodiments, the probe and coupling beams are not orthogonal.

For the illustrated case of 104.7 GHz detection, a 482 nm coupling beamcan cause the atoms in the 5P_(3/2) state (FIG. 5 ) to jump to the28D_(5/2) Rydberg state. Thus, the particles are in a superposition ofthe 5S_(1/2) ground state and the 28D_(5/2) Rydberg state. From theperspective of the probe beam, this is a “dark” superposition asparticles in neither state can absorb light of the probe wavelength (inthis case, 780 nm). In a phenomenon known as electromagnetically inducedtransparency (EIT), the coupling beam replaces with or superimposes uponthe former absorption peak a transmission peak 170 (FIG. 6 ) at theprobe laser wavelength. Transmission peak 170 can be captured by usingfrequency scanner 134 (FIG. 1 ) to modulate the frequency of probe laserbeam 160 across its center frequency; the result can be recorded usingcamera 110.

The effect of a microwave vector on the Rydberg atoms in intersection164 (FIG. 1 ) is to couple the 28D_(5/2) Rydberg state (FIG. 5 ) toanother Rydberg state 29P_(3/2). This coupling upsets the balance of thesuperposition state, and the atoms are no longer in a dark state withrespect to the probe laser. The effect on the spectrum probetransmission through the intersection is to split the transmission peak170 into a pair of transmission peaks 172, as indicated in FIG. 6 . Thefrequency difference (Δf) between the peaks 172 corresponds to theelectric field strength E₀ of the received microwave vector according toformula 154 (E₀=Δf*h/μ (FIG. 1 ), where h is Plank's constant and μ isthe dipole moment of the Rydberg atoms. Since h is a universal constantand μ is a constant for a given Rydberg state, h/μ is a constant and thefield strength of microwave vector 152 is proportional to Δf.

Detection of microwave vectors with Rydberg atoms is implemented asshown in FIG. 5 . Probe and coupling laser beams are sent through avapor cell to couple states |1

→|2

→|3

(states 5S_(1/2), 5P_(3/2), 28D_(5/2), respectively, in FIG. 5 ) toproduce Rydberg atoms and see the EIT signal (center peak 170 in FIG. 6). In the presence of a microwave field, which couples the Rydberg state|3

to a second Rydberg state |4

, the EIT peak 170 splits, yielding Autler-Townes (AT) peaks 172.

FIG. 7A presents experimental data showing that the frequencydifferences due to Autler-Townes splitting for 2.08 GHz is greater forhigher microwave power. The data in FIG. 7B demonstrates the excellentlinearity between the Autler-Townes splitting and the amplitude of theincident electric field. For each measured frequency (2.08 GHz, 6.49GHz, 12.60 GHz, and 17.84 GHz), a different pair of Rydberg levels isused, and the coupling laser wavelength is slightly changed (typically,by less than 1 nm) to access the Rydberg levels from the intermediate5P_(3/2) state. In general, lower microwave frequencies correspond tolarge dipole moments (and therefore greater measurement sensitivity).

The background atoms (outside Rydberg intersection 164) traversed byprobe laser beam 160 (FIG. 1 ) are sparse since they are loaded from asecondary MOT, (i.e. the background pressure of Rb in the second chambershould be) 10′°; therefore, they do not contribute much to the signalcaptured by camera 110. In a variation, the atoms are compressed tomaximally overlap with the Rydberg intersection to improve thesignal-to-noise ratio in images captured by camera 110. Anothervariation uses Doppler-free spectroscopy (counter-propagating laserbeams) such that only atoms that have no velocity component in thedirection of the laser beams contribute to the signal.

Thus, the microwave electric field strength within the Rydbergintersection can be determined from the probe beam spectrum, while themicrowave propagation vector direction can be determined from thelocation of the intersection of the probe and coupling beams. Todetermine the field strengths of microwave vectors from otherdirections, Rydberg intersection 164 can be moved by translating probelaser 130 and coupling laser 132 using laser steering function 136.

To obtain a two-dimensional map of field strength, i.e., determine apower distribution, as a function of direction, laser steering function136 can scan (rasterize) the lasers and thus the Rydberg intersectionacross the focal surface. Readout of the microwave field distribution isthus accomplished by performing a readout of the optical probe. Bymeasuring its spatial distribution, inferring from it the microwavefield distribution at the focal surface and applying the inverse (e.g.,Fourier) transform, the incident directions of the incoming microwavescan be determined. As mentioned above, the focusing properties of thelens can be designed for either far-field or near-field sources.

While Rydberg electrometry only works for frequencies that match one ofthe available Rydberg transitions, the spectrum of Rydberg transitionsis so dense it is almost always possible to find a transition speciesand isotope for a desired frequency. In some cases using ⁸⁷Rb, thetransition from the 28D5/2 can be to a Rydberg state other than the29P_(3/2) Rydberg state. In other cases, the first Rydberg state isother than 28D_(5/2). The table below presents a few examples forfrequencies for which experimental data is available.

Complete list of states Microwave Microwave Rydberg coupled during stateFrequency wavelength States preparation and detection. [GHz] [mm]Coupled |1> → |2> → |3> → |4> 17.04 17.59 50D_(5/2) - 51P_(3/2)5S_(1/2) - 5P_(3/2) - 50D_(5/2) - 51P_(3/2) 93.71 3.22 29D_(5/2) -30P_(3/2) 5S_(1/2) - 5P_(3/2) - 29D_(5/2) - 30P_(3/2) 104.77 2.8828D_(5/2) - 29P_(3/2) 5S_(1/2) - 5P_(3/2) - 28D_(5/2) - 29P_(3/2) 309.300.97 20D_(5/2) - 21P_(3/2) 5S_(1/2) - 5P_(3/2) - 20D_(5/2) - 21P_(3/2)

In other cases, a different particle species may be required, e.g.,cesium (¹³³Cs) atoms may be used instead of rubidium atoms. For example,the graph of FIG. 8 shows how densely packed the available Rydbergtransitions are for ¹³³Cs, especially if the principle quantum numbersfor the source and destination stats are allowed to differ by more thanunity. In other embodiments, other isotopes of rubidium and cesium maybe used, other alkali atoms may be used, and non-alkali atoms may beused. More generally, a variety of neutral and charged atoms andmolecules may be used as the cloud particles.

A microwave vector characterization process 900 is flow charted in FIG.9 . At 901, a target microwave frequency (e.g., used by certain medicalor communications equipment) or frequency range (e.g., an ITU band) isselected. At 902, various parameter values are selected based on theselected frequency or range. For example, the pitch (center-to-centerspacing) of lenslet elements of a DLA can be selected to sample signalsat the Nyquist limit. The number of elements in the lenslet array canaffect the cross-sectional dimensions of a particle-cloud cell. Inaddition, a suitable set, e.g., pair, of Rydberg states must be selectedbased on the selected frequency or range; this implies a selection of aparticle species that has those Rydberg states. Then, the laserwavelengths can be selected to produce a first of the Rydberg statesfrom which a second Rydberg state can be reached due to the impositionof a microwave vector of the target frequency.

At 903, a cloud of particles is formed. In general, this cloud is formedin a chamber; the cloud may fill the chamber or be confined, e.g., by aMOT or optical trap, to a portion of the chamber. The particles can becharged or neutral atoms or molecules that can support Rydberg stateswith high dipole moments. For example, the particles can be isotopes ofalkali atoms such as ⁸⁷Rb or ¹³³Cs. Depending on the embodiment, theparticles may be thermal, cold (below one milliKelvin, or ultracold(below 1 microKelvin). In the latter two cases, the cloud formationincludes cooling the particles, e.g., using laser cooling and/orevaporative cooling in a MOT or optical trap.

At 904, a probe laser beam is directed through the cloud and toward acamera or other imaging device. As it passes through the cloud, theprobe laser beam can excite particles from a ground or other relativelylow energy state to an intermediate energy excited state.

Concurrently, at 905, one or more coupling laser beams can be directedinto the cloud so that they intersect the probe laser beam. The effectis to transition particles from the excited state to a first Rydbergstate. The intersecting laser beams can establish an electromagneticallyinduced transparency (EIT) at the probe laser frequency. In the absenceof a microwave field, a detector or camera can detect a transmissionpeak at the probe laser wavelength.

At 906, microwave vectors of the target frequency are focused onto afocal surface within the particle cloud. Depending on the microwave lensemployed, it can be far-field or near-field signals that are focused.The microwave lens, e.g., a DLA, can be dimensioned for a particularfrequency range or band of interest. A microwave signal focused on aspot on the focal surface within the Rydberg intersection causesparticles in the first Rydberg state to transition to a second Rydbergstate. This results in an Autler-Townes splitting of the EITtransmission peak into a pair of peaks, one at a higher frequency thanthe original transmission peak and another at a lower frequency than theoriginal transmission peak.

At 907, a transmission frequency spectrum for the probe laser beam(after it has passed through the Rydberg intersection) is obtained. Forexample, frequency scanner 134 (FIG. 1 ) can sweep the frequency ofprobe laser beam through a range including both Autler-Townes peaks.Camera 110 can capture the resulting frequency spectrum. In analternative embodiment, the “camera” can be a detector with a lens and apinhole to spatially filter.

At 908, the spectrum is analyzed, e.g., by image analyzer 112, todetermine the frequency difference between the Autler-Townes peaks. At909, this frequency difference is used to calculate the microwave fieldstrength at the Rydberg intersection. The direction of the vector isdetermined from the location of the Rydberg intersection relative to thefocal surface. At 910, the Rydberg intersection is moved relative to thefocal surface to obtain a microwave power distribution across the focalsurface, and thus the field strengths and directions of microwavevectors captured by the microwave sensor.

Herein, “Rydberg particle” refers to any particle (neutral atom, ion,neutral or charged molecule, though commonly an alkali atom) species inwhich an outer electron is excited to a high-lying state. In this statethe particle has a very large electric dipole moment and can providesubstantial sensitivity for detection of a microwave field. Indeed,Rydberg particles can be used to measure microwave electric fieldamplitudes with unprecedented precision, accuracy, and spatialresolution.

Capable of operating over the microwave range, the technique of Rydbergelectrometry offers a host of benefits over measurements performed withantennas and even other quantum technologies. Signal processing can beused to manipulate and detect focal point, polarization, and phaseinformation about an incident microwave vector. For example, aroom-temperature Rydberg-atom gas produced from a 1 cm³ volume of alkalimetal vapor (e.g. Rb or Cs) is sensitive enough to detect electric-fieldamplitudes below 1 nV/cm, or three orders of magnitude greater thandipole antennas of comparable volume. Since Rydberg electrometry isbased upon the internal structure of particles, e.g., atoms, it isintrinsically accurate, eliminating the need for relative standards andperiodic instrument calibration. Rydberg electrometry has also achievedspatial resolutions approaching λ/1000 (λ is the wavelength of themicrowave vector), far better than the λ/2 or λ/4 resolutions attainablewith antennas. In an embodiment, a DLA with a known polarization is usedso that the amplitude of the electric field in the given polarizationcan be detected. Rydberg particles can be used to measure microwavepolarization to better than 1°.

Laser cooling is used to cool the Rydberg atoms to microkelvin (μK)temperatures to improve their microwave-field detection performance byminimizing Doppler effects from the atomic motion, by providingexquisite thermal isolation of the measurement sample from itsenvironment, and by increasing the numeric density of atoms thatcontribute to the EIT signal. In this context, the cold atom ensemblefurther enables the performance of the system by providing a detectionmedium that is sensitive to spatial variations in the focused microwavefield.

In contrast to superconducting devices, which require an entire physicalstructure to be cooled (typically to liquid-helium temperatures, orsometimes liquid-nitrogen in the case of high-Tc superconductors), lasercooling can be used to cool only the atoms. Laser cooling requires quitelow optical power from diode lasers, on the order of a few tens ofmilliwatts (mW), and can be performed in vacuum chambers with only a fewcubic centimeters of usable volume, thus allowing overall system size,weight, and power consumption (SWaP) to remain small.

Measurements with Rydberg atoms relate to a measurable quantity that isintrinsic to the atom. Since atoms are universal (i.e., their propertiesare the same everywhere), measurements based on their properties are notonly very accurate and stable, but are reproducible everywhere, even inspace. For this reason, atom-based sensors can be considered“self-calibrating”.

The illustrated microwave sensor design is conducive to miniaturizationand portability due to the small size of high-density cold-atom-cloudsthat can be generated. Additionally, the small size of the sensorminimally perturbs the microwave field to be measured. Finally, themethod is valuable as a completely different approach to measureelectric fields and allows for cross-checking between the differentapproaches.

Measurement using Rydberg atoms allows the conversion of a physicalquantity into a frequency. Frequencies are straightforward to measurewith high accuracy. For example, Autler-Townes splitting of ˜10 MHz(MegaHertz) can be measured with relative ease to the part-per-millionlevel, contributing negligibly to the uncertainty of electric fieldstrength E₀. This sensitivity is reflected by the large couplingstrength for microwave transitions between Rydberg states.

Rydberg atoms have transition dipole moments orders of magnitude greaterthan lower lying transitions. These enormous dipole moments give Rydbergatoms their sensitivity to electromagnetic fields in the microwave(including the millimeter) regime. The large dipole moments are also adirect result of the large distances between the valence electron andthe core. Classically, a dipole moment increases linearly with thedistance between charges. Quantum mechanically, the dipole momentincreases as n², where n is the principle quantum number of the valanceelectron.

The minimum field σ_(E) that can be measured is limited by the number ofatoms. Assuming no correlations between the atoms, the shot-noise limitis given by

${\sigma_{E} = \frac{h}{\mu\sqrt{N\tau T_{2}}}},$

where N is the number of atoms, τ is the integration time, and T₂ is thedephasing time of the EIT process. As a numerical example, consider the53D_(5/2)→54P_(3/2) transition in ⁸⁷Rb at 14.233 GHz. Let T₂˜200 μs andμ=3611 e·a₀ (e is the electron charge and a₀ is the Bohr radius).

To estimate the number of atoms, one can consider a cubic cell with aninternal volume of (100 μm)3=10-12 m3. At 80° C., the vapor pressure ofrubidium is 5×10-5 Torr, corresponding to a density of 1.5×1012 cm-3.Taking into account the 28% relative natural abundance of 87Rb, andassuming that only 1/400 of the atoms interact with the lasers due toDoppler shifts, the effective number of atoms is N≈103. The resultingsensitivity is

$\sigma_{E} \approx {460{\frac{pV}{{cm}\sqrt{Hz}}.}}$

Due to systematic effects (e.g. Doppler shifts, transit-time broadening,residual Zeeman shifts, laser intensity noise), this shot-noise limitcannot be reached easily. Nevertheless, measurements as low as 8 μV/cmhave already been achieved.

The dependency of σ_(E) on atom number is crucial for system design, asthis value decreases rapidly with cell size. In fact, for acharacteristic cell size of 100 μm, the effective number of atoms isonly 10 (at room temperature), far too small to observe. For thisreason, we assume a heated cell in the above calculation, as thisincreases the vapor pressure (i.e. atom number). The low atom density in“hot” atom systems puts a limit to the miniaturization of the system.Laser cooling and trapping offers a viable option to increase thedensity of atoms while reducing the size of the instrument.

Cooling the atoms to temperatures below a few hundred μK overcomes thesystematic effects arising from the Doppler effect seen in “hot” atomdevices. More specifically, reducing the temperature by four to sixorders of magnitude reduces the width of the atoms' velocitydistribution by the square root of this factor, or two to three ordersof magnitude. This, in turn, reduces Doppler frequency shifts to valuesbelow the natural linewidth of the atoms. From this point of view, thelaser beams can pass through the Rydberg atoms from any direction,removing constraints to a counter-propagating geometry.

Other benefits of Rydberg-atom-based electrometry over other techniquesare: 1) it directly gives the field strength in terms of a frequencymeasurement, fundamental constants, and known atomic parameters; 2) itprovides radio frequency electric field measurements independent ofcurrent techniques; 3) since no metal is present in the probe, the probecauses minimal perturbations of the field during the measurement; 4) itcan be used to measure both very weak and very strong fields over alarge range of frequencies (field strengths as low as 0.8 mV/m have beenmeasured, and below 0.01 mV/m are possible; and 5) it allows for theconstruction of very small and compact systems (optical fiber andchip-scale systems are possible).

In conventional laser measurement schemes, it is possible to obtain highspatial resolutions, but only in two dimensions (perpendicular to thelasers' axes). The lasers (and possibly the photodetector, if it is verysmall) need to be scanned to extract the information, and the techniqueis most useful when the direction of travel of the microwave field isalready known.

By using a CCD camera instead of a photodetector and using a discretelens array (DLA), one can use the images of the probe beam to obtain athree-dimensional scan of the amplitude of the electric-field and itsdirection of travel in one single measurement shot. An analytical modelcan be used to estimate the performance of the direction-finder. In theillustrated embodiment, the calculations correspond to a microwavevector of 104.7 GHz (wavelength of 2.87 mm). The calculations take intoaccount the resolution of the imaging system (CCD camera) as well as thefocusing parameters of the DLA. The position of the bright spot in thefigure can be mapped to the direction of travel of the incomingmicrowave vector. According to these calculations, it is possible todetermine the direction of travel of the incoming microwave vectors tobetter than half a degree.

The DLA (microwave lens) focuses a received microwave vector to alocation within the Rydberg intersection so as to split a transmissionpeak of the probe laser beam as it passes through the intersection. Thefrequency difference (Δ/f) between the peaks resulting from theAutler-Townes (AT) splitting is proportional to the amplitude of thereceived microwave vector. Thus, the amplitude of the microwave vectorcan be determined from a frequency spectrum obtained by frequencysweeping the probe laser beam as it is transmitted through the Rydbergparticles. The direction of the received microwave vector can bedetermined as a function of the location of the laser-beam intersection(e.g., relative to the focal surface of a microwave lens used to focusthe microwave vector).

The purpose of the DLA is to receive and focus incoming microwaveradiation into the volume of a cloud of cold Rydberg atoms. Depending onthe direction of travel of the incoming microwave vector, the DLAfocuses the microwave vector onto different locations inside the atomcloud. The resolution of propagation direction finding depends on thesize of the lens, but also on the radiation pattern of the detectorantenna elements placed along the focal surface. Some patch antennasused for detecting have effective areas that are on the order of asquare wavelength.

Adaptive-array direction finding algorithms require a much smallernumber of weights than in the case of a standard phased array due to theDFT analog front-end processing of the lens. This in turn meanslower-energy processing. Other algorithms that can easily be implementedusing the same lens include jammer-suppression and adaptive scanning.

The loss in the lens feed in receive mode is not thermal in nature,except for losses in the metal and dielectric of the lens itself andinclude spillover loss and focusing loss. The loss can be compensated byadding low-noise amplifiers (LNAs) in each element of the lens inreceive mode, and/or power amplifiers (PAs) in transmit mode. In thereceive mode, the signal combines coherently and the noise incoherently,increasing the dynamic range. In the illustrated embodiment, noamplification is used.

Although N quasi-orthogonal beams are in reality possible in anN-element lens, the number of different beams includes all linearcombinations of these N beams. Some of these are useful for directionfinding, e.g., by using two receivers on the focal surface symmetricalaround the optical axis and in phase, a null is formed on broadside andcan be used in a monopulse mode.

To image electric fields in three spatial dimensions with microwavesensor 100 (FIG. 1 ), one must selectively probe different spatialregions of the cold-atom cloud. In the one-dimensional case, themeasured image of the field gives a mapping of the field intensity overthe whole cloud, which translates to a single direction. In this scheme,the position of the lasers and the camera with respect to the DLA chipand the cloud of cold atoms determines what spatial information one canobtain. To measure the field in three dimensions, one can determine theposition of the field's focal point within the volume of the cold atomcloud.

FIG. 10A shows a three-dimensional microwave sensor 1000, which allowsfor system imaging from multiple directions to establish athree-dimensional field measurement. Sensor 1000 includes a vacuum cell1002, in which a cloud of particles is formed. Cameras 1004 and 1006 canbe used to capture frequency spectra for two different probe beams 1008and 1010, which are directed in different directions through vacuum cell1002. Coupling beams 1012 and 1014 are directed collinearly with andopposite to probe beams 1008 and 1010 respectively. The collinearity isachieved using a beam-splitting mirror 1020, as shown in FIG. 10B, whichalso shows the particle cloud 1022, an incoming microwave vector 1024, amicrowave lens 1026, and a focal surface 1028 of the microwave lens. MOTlaser beams 1030, 1032, 1034, 1036, 1038, and 1040 (FIG. 10A) are usedto form a three-dimensional MOT used to confine the particle cloud andconcentrate its constituent particles.

Using only one camera (e.g., camera 1006 in FIGS. 10A and 10B), one canextract the spatial information (direction of travel) of the incomingmicrowave signal in one direction. By using multiple cameras (e.g.cameras 1004 and 1006 in FIG. 10A) positioned at appropriate angles, andby selectively probing the atoms at discrete volumes within the cloud,it is possible to measure the full vector information of the incomingmicrowave signal (electric field strength and direction of travel) inall three spatial dimensions. Microwave sensor 1000 dynamically adjuststhe beam pointing of the probe and coupling lasers. Beam rastering canbe accomplished using steering elements, such as holograms,acousto-optic modulators, spatial light mirrors, or deformable optics.

A 3D microwave sensor process 1050 is flow-charted at FIG. 10C. At 1051,two pairs of laser beams are transmitted through a cloud of particlessuch as ⁸⁷Rb atoms. The first pair includes a first probe beam and afirst coupling beam which are counter-propagated along a first paththrough the particle cloud. The second pair includes a second probe beamand a second coupling beam which are counter-propagated along a secondpath through the particle cloud. The first and second paths intersect todefine a Rydberg intersection.

The frequencies of the probe laser beams are swept at 1052, and theresulting frequency spectra are captured at 1053. The microwave electricfield strength of the Rydberg intersection can be determined based onthe captured frequency spectra.

At 1055, a determination is made whether the “scanning” is complete. Ifthe distribution of microwave strength throughout the particle cloud isdesired, the laser beams can be steered to raster or otherwise move theRydberg intersection to discrete volumes within the particle cloud tocapture spectra and then determine microwave field strengths at thedifferent positions. Until the last position is evaluated, the survey isincomplete and process 1050 returns for a further iteration of actions1051-1054. Once the scanning is complete, the microwave field strengthscan be compiled at 1057 to obtain a microwave electric field strengthdistribution within the particle cloud.

Sensors 100 and 1000 of FIGS. 1 and 10A, respectively, use laser coolingto cool the Rydberg atoms to microkelvin temperatures to improve theirmicrowave-field detection performance by increasing local atom numberdensity, by minimizing Doppler effects from the atomic motion, and byproviding exquisite thermal isolation of the measurement sample from itsenvironment. This approach offers significant advantages in thesensitivity and resolution of existing Rydberg particle-based fieldsensors. However, the invention provides for embodiments without lasercooling where these advantages are not required.

A sensor system 1100, shown in FIG. 11A, which represents an economicalinstrument useful in less demanding applications, implements a directionfinder in a sample of un-cooled thermal atoms. Microwave sensor 1100,includes a hot vapor cell 1102 filled with a hot vapor 1104, e.g., athermal vapor of rubidium atoms, a DLA microwave lens 1106, a dichroicmirror 1108, and a detector 1110, as well as a laser system (not shown).Dichroic mirror 1108 is used to divert a probe laser beam 1112 away froma counter-propagating pump laser beam 1114 and towards detector 1110. Ina variation, a long, dense cloud is formed and used to make aone-dimensional sensor; resulting in a dramatic increase insignal-to-noise ratio.

Microwaves 1116 are incident on DLA 1106 with bilateral symmetry,forming a cylindrical lens. DLA 1106 focuses the radiation down to aline of maximal field intensity, which, in the case of a normallyincident microwave, is overlapped with a probe laser beam 1112 and acounter-propagating pump laser beam 1114. The optical field couples theatoms in the hot vapor to electronic states that are sensitive to themicrowave field, which results in a measurable change in the atomicspectroscopy.

In the case of the incoming microwave radiation 1130, FIG. 11B, beingnot normal to the surface of the DLA 1106, the DLA focuses themicrowaves onto a point 1132 located some distance away from a centralaxis, proportional to the incident angle of the radiation. As thishappens, the measured atomic spectrum will change according to thechange in angle of the radiation. An on-axis spectrum 1134 with clearlyseparated peaks and an off-axis spectrum 1136 with overlapping peaks areshown in FIG. 11B. Microwave sensor 1100 can produce an image of thecomplete spatial spectrum of the measurement region to providehigh-bandwidth direction information without the need to physically movethe device with respect to the incoming wave. The visible aperture canbe increased by using greater power in the pump beam.

Herein, a “cloud” is a collection of separate particles confined to aregion of space. The particles may be in a “gas” phase, wherein “gas”encompasses Bose gases and Fermi gases, as well as traditional gases,e.g., room-temperature vapors of neutral atoms, ions, or molecules.Herein, the “particles” can be sub-atomic particles (Bosons, Hadrons, orFermions), neutral atoms, charged atoms (ions), neutral molecules, orcharged molecules (also, “ions”).

Herein, a “microwave vector” is a propagating electric field with acharacteristic frequency between 300 MHz and 3 THz, a propagationdirection corresponding to the vector orientation, and a field strengthcorresponding to the vector magnitude. Additional characteristics of amicrowave vector can include polarization and phase. Note that thesecharacteristics may be constant or time varying. An information-bearingmicrowave vector can be a microwave signal. Microwave vectors canoverlap with a volume to collectively constitute an electric fielddistribution for the volume. Herein, a “cell” is a device for isolatingcontents within the cell from an environment outside the cell.

Herein, all art labeled “prior art”, if any, is admitted prior art; allart not labeled “prior art”, if any, is not admitted prior art. Theillustrated embodiments, variations thereupon and modifications theretoare provided for by the present invention, the scope of which is definedby the following claims.

What is claimed is:
 1. A microwave sensor process comprising: a)directing a probe laser beam and a coupling laser beam through amicrowave field populated by quantum particles, the probe laser beam andcoupling laser beam intersecting to define a Rydberg intersection withinthe microwave field such that quantum particles in a first Rydberg statetransition to a second Rydberg state; b) sweeping the frequency of theprobe laser beam to obtain a frequency spectrum for the probe beamdownstream of the Rydberg intersection; c) determining a frequencydifference between Autler-Townes-peaks based on the frequency spectrum,the Autler-Townes peaks being due to Autler-Townes splitting, and d)determining an electric-field strength of the microwave field based onthe frequency difference.
 2. The microwave sensor process of claim 1wherein: Rydberg intersections are formed at various locations withinthe microwave field, and steps a) through d) are performed at each ofthe various locations to characterize a spatial distribution ofelectric-field strength for the microwave field.
 3. The microwave sensorprocess of claim 1 wherein the probe laser beam and the coupling beamare orthogonal ±10°.
 4. The microwave sensor process of claim 1 whereinthe quantum particles are ultracold alkali atoms.
 5. The microwavesensor process of claim 1 wherein the microwave field is amillimeter-wave field.
 6. A microwave sensor system comprising: anultra-high vacuum (UHV) cell containing a microwave field and quantumparticles within the microwave field; a laser system for directing aprobe laser beam and a coupling laser beam into the UHV cell so thatthey intersect within the UHV cell to define a Rydberg intersectionwithin the microwave field, the Rydberg intersection containing quantumparticles in a first Rydberg state and a second Rydberg state; afrequency scanner for frequency sweeping the probe laser beam; an imagerfor capturing a frequency spectrum of the probe laser beam downstream ofthe Rydberg intersection; and an image analyzer for: determining afrequency difference between Autler-Townes-peaks based on the frequencyspectrum, the Autler-Townes peaks being due to Autler-Townes splitting,and determining an electric-field strength of the microwave field basedon the frequency difference.
 7. The microwave sensor system of claim 6further comprising a laser steering module for steering the probe laserbeam and the coupling laser beam so as to move the Rydberg intersectionto various positions within the UHV cell so that a spatial distributionof the electric-field strength of the microwave field can becharacterized.
 8. The microwave sensor system of claim 6 wherein theprobe laser beam and the coupling beam are orthogonal ±10°.
 9. Themicrowave sensor system of claim 6 wherein the quantum particles areultracold alkali atoms.
 10. The microwave sensor system of claim 6wherein the microwave field is a millimeter-wave field.